Group-14 elements, including C, Si, Ge, and Sn, can form various stable and metastable structures. Finding new metastable structures of group-14 elements with desirable physical properties for new technological applications has attracted a lot of interest. Using a genetic algorithm, we discovered a new low-energy metastable distorted sp(3)-hybridized framework structure of the group-14 elements. It has P4(2)/mnm symmetry with 12 atoms per unit cell. The void volume of this structure is as large as 139.7 angstrom(3) for Si P4(2)/mnm, and it can be used for gas or metal-atom encapsulation. Band-structure calculations show that P4(2)/mnm structures of Si and Ge are semiconducting with energy band gaps close to the optimal values for optoelectronic or photovoltaic applications. With metal-atom encapsulation, the P4(2)/mnm structure would also be a candidate for rattling-mediated superconducting or used as thermoelectric materials.